Brain tissue micro-structure imaging from diffusion MRI using least squares variable separation

Hamza Farooq, Junqian Xu, Essa Yacoub, Tryphon Georgiou, Christophe Lenglet

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


We introduce a novel data fitting procedure of multi compartmentmodels of the brain white matter for diffusion MRI (dMRI) data. These biophysical models aim to characterize important micro-structure quantities like axonal radius, density and orientations. In order to describe the underlying tissue properties, a variety of models for intra-/extra-axonal diffusion signals have been proposed. Combinations of these analytic models are used to predict the diffusion MRI signal in multi-compartment settings. However, parameter estimation from these multicompartment models is an ill-posed problem. Consequently, many existing fitting algorithms either rely on an initial grid search to find a good start point, or have strong assumptions like single fiber orientation to estimate some of these parameters from simpler models like the diffusion tensor (DT). In both cases, there is a tradeoff between computational complexity and accuracy of the estimated parameters. Here, we describe a novel algorithm based on the separation of the Nonlinear Least Squares (NLLS) fitting problem, via Variable Projection Method, to search for nonlinearly and linearly entering parameters independently. We use stochastic global search algorithms to find a global minimum, while estimating non-linearly entering parameters. The approach is independent of any starting point, and does not rely on estimates from simpler models. We show that the suggested algorithm is faster than algorithms involving grid search, and its greater accuracy and robustness are demonstrated on synthetic as well as ex-/in-vivo data.

Original languageEnglish
Title of host publicationComputational Diffusion MRI - MICCAI Workshop, 2015
EditorsYogesh Rathi, Andrea Fuster, Aurobrata Ghosh, Enrico Kaden, Marco Reisert
PublisherSpringer Heidelberg
Number of pages10
ISBN (Print)9783319285863
StatePublished - 2016
EventWorkshop on Computational Diffusion MRI, MICCAI 2015 - Munich, Germany
Duration: 9 Oct 20159 Oct 2015

Publication series

NameMathematics and Visualization
ISSN (Print)1612-3786
ISSN (Electronic)2197-666X


ConferenceWorkshop on Computational Diffusion MRI, MICCAI 2015


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